Question

find the length of each segment. see examples 1 and 2

1. df
2. de
3. fg
4. fh
5. gh
6. eh

Explanation:

Step1: Recall distance formula

The distance between two points $x_1$ and $x_2$ on a number - line is $d=\vert x_2 - x_1\vert$.

Step2: Find $DF$

The coordinate of $D=-4$ and the coordinate of $F = - 1\frac{1}{3}=-\frac{4}{3}$. Then $DF=\vert-\frac{4}{3}-(-4)\vert=\vert-\frac{4}{3}+4\vert=\vert\frac{-4 + 12}{3}\vert=\vert\frac{8}{3}\vert=\frac{8}{3}$.

Step3: Find $FG$

The coordinate of $F=-\frac{4}{3}$ and the coordinate of $G = 2$. Then $FG=\vert2-(-\frac{4}{3})\vert=\vert2+\frac{4}{3}\vert=\vert\frac{6 + 4}{3}\vert=\frac{10}{3}$.

Step4: Find $FH$

The coordinate of $F=-\frac{4}{3}$ and the coordinate of $H = 3\frac{1}{2}=\frac{7}{2}$. Then $FH=\vert\frac{7}{2}-(-\frac{4}{3})\vert=\vert\frac{7}{2}+\frac{4}{3}\vert=\vert\frac{21 + 8}{6}\vert=\frac{29}{6}$.

Step5: Find $GH$

The coordinate of $G = 2$ and the coordinate of $H=\frac{7}{2}$. Then $GH=\vert\frac{7}{2}-2\vert=\vert\frac{7 - 4}{2}\vert=\frac{3}{2}$.

Step6: Find $EH$

The coordinate of $E=-1\frac{1}{3}=-\frac{4}{3}$ and the coordinate of $H=\frac{7}{2}$. Then $EH=\vert\frac{7}{2}-(-\frac{4}{3})\vert=\vert\frac{7}{2}+\frac{4}{3}\vert=\frac{29}{6}$.

Answer:

1. $\frac{8}{3}$
2. $\frac{10}{3}$
3. $\frac{29}{6}$
4. $\frac{3}{2}$
5. $\frac{29}{6}$